There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The concepts of the conventional theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are illustrated in the context of a simple example---the phase separation of a symmetric binary fluid. The renormalization group is then developed in some detail, and applied to a variety of systems. The main dynamic universality classes are identified and characterized. It is found that the mode-coupling and renormalization group theories successfully explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies exist with data at the superfluid transition of $^{4}\mathrm{He}$.

Theory of Dynamic Critical Phenomena

Magnetoencephalography (MEG) is a noninvasive technique for investigating neuronal activity in the living human brain. The time resolution of the method is better than 1 ms and the spatial discrimination is, under favorable circumstances, 2-3 mm for sources in the cerebral cortex. In MEG studies, the weak 10 fT-1 pT magnetic fields produced by electric currents flowing in neurons are measured with multichannel SQUID (superconducting quantum interference device) gradiometers. The sites in the cerebral cortex that are activated by a stimulus can be found from the detected magnetic-field distribution, provided that appropriate assumptions about the source render the solution of the inverse problem unique. Many interesting properties of the working human brain can be studied, including spontaneous activity and signal processing following external stimuli. For clinical purposes, determination of the locations of epileptic foci is of interest. The authors begin with a general introduction and a short discussion of the neural basis of MEG. The mathematical theory of the method is then explained in detail, followed by a thorough description of MEG instrumentation, data analysis, and practical construction of multi-SQUID devices. Finally, several MEG experiments performed in the authors' laboratory are described, covering studies of evoked responses and of spontaneous activity in both healthy and diseased brains. Many MEG studies by other groups are discussed briefly as well.

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Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain

Anyons in an exactly solved model and beyond

This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

It is shown that nanoparticles made of very low-${T}_{c}$ superconductors have a large diamagnetic response at temperatures several orders of magnitude above ${T}_{c}$. Most of the features of the recently observed giant diamagnetism of Au nanorods are explained in terms of superconducting fluctuations, except for the huge magnitude of the effect.

Superconducting fluctuations and large diamagnetism of low- T c nanoparticles

Dephasing of Interference by a Back Reacting Environment

The enhancement of electronic transport in the localized regime by the electron-electron interactions is discussed both in the incoherent channel, leading to transport via inelastic scattering, and in the coherent channel, via delocalization. For the former channel, a new prediction for the temperature dependence of the conductivity in a weak granular insulator is given. The conditions for an effective decay of a given state weakly coupled to a quasicontinuum are obtained. This is applied to both the decay of a singleelectron excited state due to interactions and to interblock transport in the scaling theory of localization. Thus the latter theory can include some of the effects of the interactions. Two-electron delocalization is a good example for that, which is also treated in this paper.

Delocalization, Inelastic Scattering and Transport due to Interactions

Glassy systems are ubiquitous in nature, and are characterized by slow relaxations to equilibrium without a typical timescale, aging and memory effects. Understanding these is a long-standing problem in physics. We study the aging of the electron glass, a system showing remarkable slow relaxations in the conductance. We find that the broad distribution of relaxation rates leads to a universal relaxation of the form log(1+t_w/t) for the usual aging protocol, where t_w is the length of time the perturbation driving the system out-of-equilibrium was on, and t the time of measurement. These results agree well with several experiments performed on different glasses, and examining different physical observables, for times ranging from seconds to several hours. The suggested theoretical framework appears to offer a paradigm for aging in a broad class of glassy materials.

A new universality class of aging in glassy systems

For a variety of quantum dots, the widths of different single-particle levels may naturally differ by orders of magnitude. In particular, the width of one strongly coupled level may be larger than the spacing between other, very narrow, levels. We found that in this case many consecutive Coulomb blockade peaks are due to occupation of the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation of the salient features of the behavior of the transmission phase in an interferometer with a QD. The theory of this effect will be reviewed with special emphasis on the role of the interactions. New results on the dot-charging measurements and the fine structure of occupation switchings will be presented, accompanied by the unified description of the whole series of CB peaks caused by a single broad level. We then discuss the case where the system approaches the Kondo regime.

Yoseph Imry

Papers

Superconducting fluctuations and large diamagnetism of low- T c nanoparticles

Dephasing of Interference by a Back Reacting Environment

Delocalization, Inelastic Scattering and Transport due to Interactions

A new universality class of aging in glassy systems

Level-occupation switching of the Quantum Dot, and phase anomalies in mesoscopic interferometry